Zheng Qunxian, Xu Shengyuan, Du Baozhu
IEEE Trans Cybern. 2023 Dec;53(12):7966-7979. doi: 10.1109/TCYB.2023.3253161. Epub 2023 Nov 29.
This work researches the resilent mixed H and energy-to-peak filter design problem of switched Takagi-Sugeno (T-S) fuzzy systems with asynchronous switching and multiple state impulsive jumps. The novelties include three points. First, a novel mixed H and energy-to-peak performance index is proposed, which covers the H performance index and energy-to-peak performance index as special cases. Second, in addition to designing the switching filters, the filter state jump rules are constructed at filter switching instants. Finally, both system states and filter states jump in a asynchronous manner. The switching law is devised through the mode-dependent average dwell time (MDADT) approach. A new type of Lyapunov-like functionals is constructed, which will increase when the subsystem is running with its mismatched filter and jump while the subsystem or the filter is switching. Then, new conditions are deduced to ensure the filtering error systems with multiple state impulsive jumps to be asymptotically stable with a mixed H and energy-to-peak performance level. Filter design conditions expressing as linear matrix inequality (LMI) are obtained. Finally, the effectiveness of the derived results is illustrated by two examples.
本文研究了具有异步切换和多状态脉冲跳变的切换Takagi-Sugeno（T-S）模糊系统的弹性混合H和能量到峰值滤波器设计问题。其新颖之处包括三点。首先，提出了一种新颖的混合H和能量到峰值性能指标，它将H性能指标和能量到峰值性能指标作为特殊情况涵盖在内。其次，除了设计切换滤波器外，还在滤波器切换时刻构建了滤波器状态跳变规则。最后，系统状态和滤波器状态均以异步方式跳变。通过基于模式的平均驻留时间（MDADT）方法设计切换律。构造了一种新型的类Lyapunov泛函，当子系统与不匹配的滤波器一起运行且在子系统或滤波器切换时跳变时，该泛函会增加。然后，推导了新的条件，以确保具有多状态脉冲跳变的滤波误差系统在混合H和能量到峰值性能水平下渐近稳定。得到了以线性矩阵不等式（LMI）表示的滤波器设计条件。最后，通过两个例子说明了所得结果的有效性。
